In Magnetic Resonance Imaging (MRI), images are reconstructed from k-space measurements. Because images are usually highly compressible in some transform domain, one can “compress” or undersample the measurements before reconstruction. This process of reconstructing images from very few measurements is referred to as “Compressed Sensing (CS).” Compressed Sensing is a preferred technique for acquiring MRI images because it reduces the time of acquiring measurements, and thus patients receive much less radiation compared to other acquisition techniques.
Conventional Compressed Sensing (CS) techniques are based on convex optimization algorithms such as Fast Iterative Soft-Thresholding (FISTA) or Alternating Direction Method Of Multipliers (ADMM). Those algorithms usually solve the problem from maximum a posteriori (MAP) point of view and do not provide any information about the confidence of the reconstruction—i.e., the measure of differences between the reconstructed image and the ground-truth. However, confidence information would greatly aid in the diagnosis process. For example, such information would allow physicians to quickly access whether a particular item in an image is anatomical in nature (e.g., a lesion) or if it is merely potential artifact. Additionally, confidence information can be used to optimize the reconstruction itself, by providing a measure of how many iterations are needed to provide fidelity in the area of interest. Accordingly, it is desired to create a reconstruction technique suitable for Compressed Sensing (CS) application that produces both the reconstructed image, along with measure of confidence in the reconstructed data.